Three-dimensional absolute and convective instabilities in mixed convection of a viscoelastic fluid through a porous medium

By using the mathematical formalism of absolute and convective instabilities we study the nature of unstable three-dimensional disturbances of viscoelastic flow convection in a porous medium with horizontal through-flow and vertical temperature gradient. Temporal stability analysis reveals that among three-dimensional (3D) modes the pure down-stream transverse rolls are favored for the onset of convection. In addition, by considering a spatiotemporal stability approach we found that all unstable 3D modes are convectively unstable except the transverse rolls which may experience a transition to absolute instability. The combined influence of through-flow and elastic parameters on the absolute instability threshold, wave number and frequency is then determined, and results are compared to those of a Newtonian fluid.     

Three-dimensional electrohydrodynamic temporal instability of a moving dielectric liquid sheet emanated into a gas medium

A linear electrohydrodynamic instability analysis is presented for an inviscid dielectric liquid sheet emanated into an inviscid dielectric gas medium in the presence of a horizontal electric field. The influence of Weber number, gas-to-liquid density ratio, and the applied electric field on the evolution of two-, and three-dimensional disturbances of symmetrical and antisymmetrical types is studied. It is found, for antisymmetrical waves, that two-dimensional disturbances always prevail over three-dimensional disturbances, regardless of Weber number or gas-to-liquid density ratio values, especially for long waves; while for short waves, both two- and three-dimensional disturbances grow at approximately the same rate. It is also found, for symmetrical waves, that two-dimensional disturbances always dominate the instability process at low Weber number, and when the Weber number is large, symmetrical three-dimensional disturbances become more unstable than two-dimensional ones for long waves. The effect of increasing the gas-to-liquid density ratio is to promote the dominance of long three-dimensional symmetrical waves over their two-dimensional counterpart. Finally, the equilibrium Weber number at which the growth rates of two- and three-dimensional modes are equal is discussed for both symmetrical- and antisymmetrical-disturbances cases.-1     

同轴流动聚焦中射流不稳定性的理论研究

壳核结构的微胶囊在医学药学材料食品农业等领域具有广泛的应用前景, 其制备方法一直是相关领域关注的焦点.同轴流动聚焦(co-flow focusing)是一种新型制备技术, 利用复合射流的破碎制备微胶囊具有包裹率高过程量化可控参数域广产率高等诸多优势.在实验中, 复合射流的破碎受到多个过程参数的影响, 并涉及了多层界面的耦合效应.利用简化的物理模型, 在时间和时空域中分析了三相水-油-水复合射流不稳定性的发展和演化.在黏性流体线性稳定性理论中, 同轴射流和驱动液体的基本速度型分别基于管流和误差函数构造, 并通过数值方法求解满足相应边界条件下的线化小扰动控制方程.结果表明:增加内外层界面的界面张力均有利于射流的破碎; 流体的黏性对同轴射流的稳定性均有着促进作用; 越大的黏性越小的内界面张力对应着越大的射流破碎波长; 内外界面的耦合作用以及复合液滴的包裹情况均与内外射流的半径比息息相关; 绝对-对流不稳定性转换的临界Weber数随Reynolds数内层界面张力的增大而增大, 随内层和驱动流体的黏性增大而减小.这些结果将有助于提高液体驱动下同轴流动聚焦技术的过程控制, 为实际应用提供理论指导.      

On bending instability of a volumetrically charged capillary jet of dielectric liquids

It is shown that jets of volumetrically charged dielectric liquids in the vicinity of point k = 0 are characterized by a finite range of wavenumbers, in which a jet exhibits bending instability. The interval of wavenumbers corresponding to unstable waves with azimuth number m = 1, as well as the increment of the most unstable wave and its wavenumber, increase in proportional to the electric charge per unit length of the jet and the permittivity of the liquid.     

On the theory of instabilities arising at quark-gluon plasma formation

Collisions of two degenerate quark Fermi liquids are studied. It is shown that there arise instabilities, which manifest themselves in propagation of growing oscillations corresponding to the modes existing in a Fermi liquid at rest. Quark jets are likely to appear in the directions of the growing oscillations propagation.

The instabilities studied in this work are similar to the beam instability in ordinary electron plasma.     

Instabilities in a two-dimensional polar-filament-motor system

The dynamical interaction between filaments and motor proteins is known for their propensity to self-organize into spatio-temporal patterns. Since the filaments are polar in the sense that motors define a direction of motion on them, the system can display a spatially homogeneous polar-filament orientation. We show that the latter anisotropic state itself may become unstable with respect to inhomogeneous fluctuations. This scenario shares similarities with instabilities in planarly aligned nematic liquid crystals: in both cases the wave vector of the instability may be oriented either parallel or oblique to the polarity axis. However, the encountered instabilities here are long-wave instead of short-wave and the destabilizing modes are drifting ones due to the polar symmetry. Additionally a nonpropagating transverse instability is possible. The stability diagrams related to the various wave vector orientations relative to the polarity axis are determined and discussed for a specific model of motor-filament interactions.     

Multistream instability of crossed electron beams in a plasma

Multistream instabilities of crossed electron beams in a plasma are investigated analytically. By using successively more complicated models, the instability of a finite number of crossed monoenergetic beams and the instability of an infinite number of crossed monoenergetic beams with different distributions in the azimuthal angle are studied. The conclusion is drawn that an isotropic plasma is unstable against the excitation of longitudinal waves.     

Temperature effects on capillary instabilities in a thin nematic liquid crystalline fiber embedded in a viscous matrix

Linear stability analysis of capillary instabilities in a thin nematic liquid crystalline cylindrical fiber embedded in an immiscible viscous matrix is performed by formulating and solving the governing nemato-capillary equations, that include the effect of temperature on the nematic ordering as well as the effect of the nematic orientation. A representative axial nematic orientation texture with the planar easy axis at the fiber surface is studied. The surface disturbance is expressed in normal modes, which include the azimuthal wave number m to take into account non-axisymmetric modes. Capillary instabilities in nematic fibers reflect the anisotropic nature of liquid crystals, such as the ordering and orientation contributions to the surface elasticity and surface normal and bending stresses. Surface gradients of normal and bending stresses provide additional anisotropic contributions to the capillary pressure that may renormalize the classical displacement and curvature forces that exist in any fluid fiber. The exact nature (stabilizing and destabilizing) and magnitude of the renormalization of the displacement and curvature forces depend on the nematic ordering and orientation, i.e. the anisotropic contribution to the surface energy, and accordingly capillary instabilities may be axisymmetric or non-axisymmetric. In addition, when the interface curvature effects are accounted for as contributions of the work of interfacial bending and torsion to the total energy of the system, the higher-order bending moment contribution to the surface stress tensor is critical in stabilizing the fiber instabilities. For the planar easy axis, the nematic ordering contribution to the surface energy, which renormalizes the effect of the fiber shape, plays a crucial role to determine the instability mechanisms. Moreover, the unstable modes, which are most likely observed, can be driven by the dependence of surface energy on the surface area. Low-ordering fibers display the classical axisymmetric mode, since the surface energy decreases by decreasing the surface area. Decreasing temperature gives rise to the encounter with a local maximum or to monotonic increase of the characteristic length of the axisymmetric mode. Meanwhile, in the presence of high surface ordering, non-axisymmetric finite wavelength instabilities emerge, with higher modes growing faster since the surface energy decreases by increasing the surface area. As temperature decreases, the pitches of the chiral microstructures become smaller. However, this non-axisymmetric instability mechanism can be regulated by taking account of the surface bending moment, which contains higher order variations in the interface curvatures. More and more non-axisymmetric modes emerge as temperature decreases, but, at constant temperature, only a finite number of non-axisymmetric modes are unstable and a single fastest growing mode emerges with lower and higher unstable modes growing slower. For nematic fibers, the classical fiber-to-droplet transformation is one of several possible instability pathways, while others include chiral microstructures. The capillary instabilities' growth rate of a thin nematic fiber in a viscous matrix is suppressed by increasing either the fiber or matrix viscosity, but the estimated droplet sizes after fiber breakup in axisymmetric instabilities decrease with increasing the matrix viscosity. Received 15 April 2002 and Received in final form 3 October 2002 RID="a" ID="a"e-mail: alejandro.rey@mcgill.ca     

Noise generation by instabilities in low Reynolds number supersonic jets

An experimental investigation of noise generation by instabilities in low Reynolds number supersonic air jets has been performed. Sound pressure levels, spectra and acoustic phase fronts were measured with a traversing condenser microphone in the acoustic field of axisymmetric, perfectly expanded, cold jets of Mach numbers 1·4, 2·1 and 2·5. Low Reynolds numbers in the range from Re = 3700 to Re = 8700 were obtained by exhausting the jets into an anechoic vacuum chamber test facility. This contrasts with Reynolds numbers of over 10⁶ for similar jets exhausting into atmospheric pressure. The flow fluctuations of the instability in all three jets have been measured with a hot-wire and the results are documented in a previous paper by Morrison and McLaughlin. Acoustic measurements show that the major portion of the sound radiated by all three jets is produced by the instability's rapid growth and decay that occurs near the end of the potential core. This takes place over a relatively short distance (less than two wavelengths of the instability) in the jet. In the lower two Mach number jets the instability has a phase velocity less than the ambient acoustic velocity. In the Mach number 2·5 jet the instability phase speed is 1·11 times the ambient acoustic velocity. In this case the acoustic phase fronts indicate the possibility of a Mach wave component. It was also determined that low level excitation at the dominant frequency of the instability actually decreased the radiated noise by suppressing the broad band component.     

Magnetorotational-type instability in Couette-Taylor flow of a viscoelastic polymer liquid

We describe an instability of viscoelastic Couette-Taylor flow that is directly analogous to the magnetorotational instability (MRI) in astrophysical magnetohydrodynamics, with polymer molecules playing the role of magnetic field lines. By determining the conditions required for the onset of instability and the properties of the preferred modes, we distinguish it from the centrifugal and elastic instabilities studied previously. Experimental demonstration and investigation should be much easier for the viscoelastic instability than for the MRI in a liquid metal. The analogy holds with the case of a predominantly toroidal magnetic field such as is expected in an accretion disk, and it may be possible to access a turbulent regime in which many modes are unstable.     

Influence of charge relaxation on the capillary disintegration of a jet of a viscous dielectric liquid placed in an electrostatic field collinear with the axis of the jet

A dispersion relation is derived for capillary waves with an arbitrary symmetry on the surface of a charged jet of a finite-conductivity viscous liquid placed in an electric field collinear with the axis of the jet. Analytical calculations are carried out in an approximation that is linear in dimensionless wave amplitude. In the case of axisymmetric waves, the instability of which causes disintegration of the jet into drops, the finiteness of the potential equalization rate has a noticeable effect only for jets of poorly conducting liquids. The charge relaxation shows up in that “purely relaxation” periodic and aperiodic liquid flows arise. When the conductivity of the liquid declines, the instability growth rates for unstable waves increase and their spectrum extends toward short waves. A charge present on the surface of the jet enhances its instability. An increase in the charge surface diffusion coefficient variously influences the capillary and relaxation branches of the solution: the damping ratio increases in the former case and decreases in the latter. As the diffusion coefficient rises, relaxation flows may become unstable.     

Modeling multi-jet mode electrostatic atomization using boundary element methods

A two-dimensional, nonlinear model has been developed to assess the dynamics of charged liquid columns. The model, which is based on the boundary element method (BEM), has been used to investigate oscillations and instabilities of single and multi-column configurations. For the single-column configuration, oscillation frequencies have been determined for a range of charge and initial distortion levels. In addition, simulations of unstable jets have been conducted; these results show a “spiked” behavior at the pinching event. An energy-based analysis has been used to determine maximum voltages for stable configurations with a given number of ligaments. These results are compared against experimental data.     

Spectral characteristics of unstable flow in the mixing layer of supersonic underexpanded jet over its initial region

An experimental study of spectral characteristics of unstable flow in the mixing layer of supersonic axisymmetric underexpanded jets with Mach number M_a = 1 is reported. The destabilization of the flow is related to the formation, in the mixing layer of the jets, of disturbances in the form of streamwise vortical structures of the Taylor — Goertler type. As a result, in the mixing layer there forms an azimuthally non-uniform stationary distribution of total pressure. The Fourier transform of azimuthal sweeps of non-uniformity in pressure distributions was used to calculate the amplitude-wave spectra. An analysis of the spectral characteristics has allowed us to evaluate the longitudinal increment of amplitude growth of the disturbances and their dependence on the wavenumber and on the nozzle pressure ratio. The range of wavenumbers in which the streamwise vortical structures grow in amplitude is identified. This work was financially supported by the Russian Foundation for Basic Research (Grant No. 05-08-01215).     

Experimental evidence of a Rayleigh-plateau instability in free falling granular jets

A granular jet falling out of a funnel shaped container, subjected to small vertical vibrations, develops an instability farther downstream as may happen for ordinary liquid jets. Our results show that this instability is reminiscent of the Rayleigh-Plateau capillary instability leading to breakup of the jet at large scales. The first stages of this instability are captured in detail allowing a determination of the dispersion relation. Surface tensions measured in this unstable regime (of the order of mN/m) are in agreement with previously reported measurements carried out at much smaller scales. This instability and the breakup of the jet can be inhibited when the effect of the surrounding medium (air) is reduced by enclosing the jet in an evacuated chamber, showing that the effective surface tension measured is the result of a strong interaction with the surrounding air.     

Electrocapillary instability of a conducting liquid cylinder

The electrocapillary instability of a conducting liquid cylinder is analyzed. Exact solutions to the linearized Navier-Stokes equations are examined. Growth rates are found for several unstable modes, including both axisymmetric and nonaxisymmetric ones. Special attention is given to the electric field effects on the temporal growth and length scales of unstable modes. It is shown that, whereas capillary instability is axisymmetric in the absence of electric field, nonaxisymmetric surface modes also become unstable in a nonzero electric field, growing with time. With increasing electric field strength, azimuthal modes are “switched on” (begin to grow with time) sequentially and the highest temporal growth rate monotonically increases.     

The Coulomb instability of charged microdroplets: dynamics and scaling

The stability and disintegration dynamics of evaporating highly charged liquid droplets from ethylene glycol and glycerol is investigated by ultrafast microscopy and analyzed as a function of temperature and droplet size. In the moment of instability the droplets have deformed to elongated spindle like shapes from which pairs of opposite jets of highly charged liquid are emitted. The thickness of the jets and the shape of the deformed droplet are remarkably insensitive to the size and viscosity of the unstable droplet, while the speed of disintegration is found to scale with a power law for both variables, the exponent being close to 3/2.     

液滴超声速气动破碎初期界面不稳定性

针对液滴破碎问题,获得并揭示两相界面演化特征机理.采用数值模拟方法,观察了超声速条件下的液滴气动破碎初期的界面不稳定性.基于数值模拟结果和线性稳定性理论,综合分析表明,Rayleigh-Taylor不稳定性和Kelvin-Helmholtz不稳定性均对源于驻点和外环之间中段附近处的主导扰动产生作用.保持其他流动特性不变,降低K-H不稳定性的影响,对数值模拟进行了专门改进,进一步验证了前述结论.      

A piecewise linear mean flow model for studying stability in a lined channel

Acoustic liners are used to reduce sound emission by turbofan engines. Under grazing flow they may sustain hydrodynamic instabilities and these are studied using a stability analysis, based on a simplified model: the liner is a mass–spring–damper system, the base channel flow is piecewise linear, and the inviscid, incompressible Rayleigh equation is used. The model is an extension to the channel case of a boundary layer model by Rienstra and Darau. The piecewise linear profile introduces a finite boundary layer thickness which ensures well-posedness, allowing an initial value problem to be conducted to investigate absolute stability. For typical values in aeronautics the flow above the liner is unstable. Absolute instability is obtained for somewhat extreme values of the mean flow (tiny boundary layer thickness), and under realistic conditions the flow is convectively unstable. The effect of finite channel height is investigated in both cases. In particular, for large boundary layer thicknesses associated with convective instability the channel height has little effect on the unstable mode. Favorable outcomes and failures of the model are shown by comparison to a published experimental work.     

Instabilities in Yukawa Liquids

A strongly coupled Yukawa liquid is a system of charged particles which interact via a screened Coulomb interaction and in which the electrostatic energy between neighboring particles is larger than their thermal energy but not large enough for crystallization. Various plasma systems including ultracold neutral plasmas and complex (dusty) plasmas can exist in this strongly coupled liquid phase.Here we investigate instabilities driven by the relative streaming of plasma components in three‐dimensional Yukawa liquids with a focus on complex plasmas. This includes a dust acoustic instability driven by weakly coupled ions streaming through the dust liquid, and a dust‐dust instability driven by the counter‐streaming of strongly coupled dust grains. Compared to the Vlasov behavior we find there can be a substantial modification of the unstable wavenumber spectrum due to strong coupling effects (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parallel flow in hele-shaw cells with ferrofluids

Parallel flow in a Hele-Shaw cell occurs when two immiscible liquids flow with relative velocity parallel to the interface between them. The interface is unstable due to a Kelvin-Helmholtz type of instability in which fluid flow couples with inertial effects to cause an initial small perturbation to grow. Large amplitude disturbances form stable solitons. We consider the effects of applied magnetic fields when one of the two fluids is a ferrofluid. The dispersion relation governing mode growth is modified so that the magnetic field can destabilize the interface even in the absence of inertial effects. However, the magnetic field does not affect the speed of wave propogation for a given wave number. We note that the magnetic field creates an effective interaction between the solitons.